Validation of Delamination Reduction Trend for Stitched Composites using Quasi-Static Indentation Test

A novel empirical-based Delamination Reduction Trend (DRT) for stitched composites has been recently proposed. The DRT is capable of predicting the effective reduction in impact induced delamination area due to the influence of stitching. DRT simply relates two parameters: normalized delamination area and stitch fibre volume fraction, to characterize the effectiveness of stitching in impact damage suppression. This paper seeks to validate the DRT by using quasi-static indentation (QSI) test, which is considered analogous to low velocity impact test, due to similar structural response. Results from QSI test show good agreement with DRT. Furthermore, limitations in DRT have been established

Progressive Damage in Stitched Composites under Impact Loading

Damage in carbon fibre reinforced plastics (CFRP) due to impact loading is an extremely complex phenomenon that comprises of multiple failure mechanisms like intra-laminar matrix cracks, interlaminar delamination, fibre pull-out and fibre fracture. In stitched composites, impact damage behavior is further complicated by the presence of through-thickness stitching [1, 2], which not only favorably increases mode I/II interlaminar strength [3, 4], but also inevitably creates geometrical defects like weak resin-rich pockets around stitch threads and misalignment of in-plane fibres. Computational modeling has been used to simulate progressive damage effectively [5]. However, the complexity of impact damage progression in stitched composites would need to be first understood and appreciated by physical experimental observations. In this study, quasi-static indentation (QSI) test is performed for the first time on stitched composites. QSI offers a good validation and comparison with low-velocity impact (LVI) test [6], and provides good understanding on damage progression in composite structures under impact loading. Damage initiation, propagation and ultimate failure are investigated due to the effect of stitching, particularly the influence of stitch density. Nondestructive evaluation (NDE) techniques namely ultrasonic c-scan analysis, x-ray radiography and xray micro computed tomography are employed to elucidate various damage mechanisms in stitched composites

Gauss decomposition for Chevalley groups, revisited

In the 1960's Noboru Iwahori and Hideya Matsumoto, Eiichi Abe and Kazuo Suzuki, and Michael Stein discovered that Chevalley groups $G=G(\Phi,R)$ over a semilocal ring admit remarkable Gauss decomposition $G=TUU^-U$, where $T=T(\Phi,R)$ is a split maximal torus, whereas $U=U(\Phi,R)$ and $U^-=U^-(\Phi,R)$ are unipotent radicals of two opposite Borel subgroups $B=B(\Phi,R)$ and $B^-=B^-(\Phi,R)$ containing $T$. It follows from the classical work of Hyman Bass and Michael Stein that for classical groups Gauss decomposition holds under weaker assumptions such as \sr(R)=1 or \asr(R)=1. Later the second author noticed that condition \sr(R)=1 is necessary for Gauss decomposition. Here, we show that a slight variation of Tavgen's rank reduction theorem implies that for the elementary group $E(\Phi,R)$ condition \sr(R)=1 is also sufficient for Gauss decomposition. In other words, $E=HUU^-U$, where $H=H(\Phi,R)=T\cap E$. This surprising result shows that stronger conditions on the ground ring, such as being semi-local, \asr(R)=1, \sr(R,\Lambda)=1, etc., were only needed to guarantee that for simply connected groups $G=E$, rather than to verify the Gauss decomposition itself

Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page

Development of a simultaneous analytical method for five conjugated cholesterol metabolites in urine and investigation of their performance as diagnostic markers for Niemann-Pick disease type C

Niemann-Pick disease type C (NPC) is an autosomal recessive disorder characterized by progressive nervous degeneration. Because of the diversity of clinical symptoms and onset age, the diagnosis of this disease is difficult. Therefore, biomarker tests have attracted significant attention for earlier diagnostics. In this study, we developed a simultaneous analysis method for five urinary conjugated cholesterol metabolites, which are potential diagnostic biomarkers for a rapid, convenient, and noninvasive chemical diagnosis, using liquid chromatography/tandem mass spectrometry (LC/MS/MS). By the method, their urinary concentrations were quantified and the NPC diagnostic performances were evaluated. The developed LC/MS/MS method showed high accuracy and and satisfied all analytical method validation criteria. Analyzing the urine of healthy controls and patients with NPC, three of five urinary conjugated cholesterol metabolites concentrations corrected by urinary creatinine were significantly higher in the patients with NPC. As a result of receiver operating characteristics analysis, the urinary metabolites might have excellent diagnostic marker performance. 3β-sulfooxy-7β-hydroxy-5-cholenoic acid showed particularly excellent diagnostic performance with both 100% clinical sensitivity and specificity, suggesting that it is a useful NPC diagnostic marker. The urinary conjugated cholesterol metabolites exhibited high NPC diagnostic marker performance and could be used for NPC diagnosis

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

The classification of irreducible admissible mod p representations of a p-adic GL_n

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over \bar F_p in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livne for n = 2. For general split reductive groups we obtain similar results under stronger hypotheses.Comment: 55 pages, to appear in Inventiones Mathematica

Infinite-dimensional pp-adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings

We construct $p$-adic analogs of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty, Q_p)$, its subgroup $L=O(k\infty,Z_p)$, and the subgroup $K=O(\infty,Z_p)$ embedded to $L$ diagonally. We show that double cosets $\Gamma= K\setminus G/K$ admit a structure of a semigroup, $\Gamma$ acts naturally in $K$-fixed vectors of unitary representations of $G$. For each double coset we assign a 'characteristic function', which sends a certain Bruhat--Tits building to another building (buildings are finite-dimensional); image of the distinguished boundary is contained in the distinguished boundary. The latter building admits a structure of (Nazarov) semigroup, the product in $\Gamma$ corresponds to a point-wise product of characteristic functions.Comment: new version of the paper, 47pp, 3 figure

Structural Determination of Lysosphingomyelin-509 and Discovery of Novel Class Lipids from Patients with Niemann–Pick Disease Type C

Niemann–Pick disease type C (NPC) is an autosomal recessive disorder caused by the mutation of cholesterol-transporting proteins. In addition, early treatment is important for good prognosis of this disease because of the progressive neurodegeneration. However, the diagnosis of this disease is difficult due to a variety of clinical spectrum. Lysosphingomyelin-509, which is one of the most useful biomarkers for NPC, was applied for the rapid and easy detection of NPC. The fact that its chemical structure was unknown until recently implicates the unrevealed pathophysiology and molecular mechanisms of NPC. In this study, we aimed to elucidate the structure of lysosphingomyelin-509 by various mass spectrometric techniques. As our identification strategy, we adopted analytical and organic chemistry approaches to the serum of patients with NPC. Chemical derivatization and hydrogen abstraction dissociation–tandem mass spectrometry were used for the determination of function groups and partial structure, respectively. As a result, we revealed the exact structure of lysosphingomyelin-509 as N-acylated and O-phosphocholine adducted serine. Additionally, we found that a group of metabolites with N-acyl groups were increased considerably in the serum/plasma of patients with NPC as compared to that of other groups using targeted lipidomics analysis. Our techniques were useful for the identification of lysosphingomyelin-509

Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric